Group Policies and groups are two completely different things.
And yes, I know the names are misleading.
A Group Policy Object is a set of policies linked to one or more Organizational Units in Active Directory; they will affect all computer and/or users in that container and below (there are exceptions, but this is the core concept).
A group is, just like the name implies, a collection of users, computers or other groups; it can be located anywhere in AD, and its members also can be located anywhere. It's mainly used for security, because assigning permissions to a group is a lot easier than doing the same for each individual user (but it can also act as a mail distribution list where Exchange is in use).
To manage Groups Policies, you use the Group Policy Management Console.
To manage groups (or users, or computers, or Active Directory in general) you use Active Directory Users and Computers.
If you need to check who is member of a given group, ADUC is the right tool to use; GPMC will not tell you anything about that, because it's not its job.
ADUC is always present on Domain Controllers, and can be installed on Windows Server systems as a feature (part of AD DS Tools).
If you want to use it on a client system, you'll need to install Remote Server Administration Tools.
Addendum: the net group command applies to groups, which as I said above are different from GPOs. It doesn't make any sense to run net group my_gpo.
You're running into a design-limitation of Offline Files. It is a per-machine cache, enabled and disabled at a per-machine level. Offline Files limits visibility of items to users who are authorized to view them, but there is a single cache on the machine. You can't disable the caching functionality for just certain users on a machine.
There just isn't a granular level of control to do what you're looking for. The community asked for it in Windows Vista, again in Windows 7, and still didn't get it in Windows 8. (There's some kinda, sorta functionality in Windows 8 with the "Primary Computer" functionality of Folder Redirection, but that's not a change in Offline Files-- it's just a change in Folder Redirection that impacts the Group Policy setting to always make redirected folders available offline as a side-effect.)
Best Answer
In the section of GPO you mentioned, I see a policy named:
This sounds exactly like what you're trying to achieve unless I'm missing something.